private static bool IsSquare(uint[] x)
{
uint[] t1 = Nat224.Create();
uint[] t2 = Nat224.Create();
Nat224.Copy(x, t1);
for (int i = 0; i < 7; ++i)
{
Nat224.Copy(t1, t2);
SecP224R1Field.SquareN(t1, 1 << i, t1);
SecP224R1Field.Multiply(t1, t2, t1);
}
SecP224R1Field.SquareN(t1, 95, t1);
return(Nat224.IsOne(t1));
}
/**
* return a sqrt root - the routine verifies that the calculation returns the right value - if
* none exists it returns null.
*/
public override ECFieldElement Sqrt()
{
uint[] c = this.x;
if (Nat224.IsZero(c) || Nat224.IsOne(c))
{
return(this);
}
uint[] nc = Nat224.Create();
SecP224R1Field.Negate(c, nc);
uint[] r = Mod.Random(SecP224R1Field.P);
for (;;)
{
uint[] d1 = Nat224.Create();
Nat224.Copy(r, d1);
uint[] e1 = Nat224.Create();
e1[0] = 1;
uint[] f1 = Nat224.Create();
RP(nc, d1, e1, f1);
uint[] d0 = Nat224.Create();
uint[] e0 = Nat224.Create();
for (int k = 1; k < 96; ++k)
{
Nat224.Copy(d1, d0);
Nat224.Copy(e1, e0);
RS(d1, e1, f1);
if (Nat224.IsZero(d1))
{
Mod.Invert(SecP224R1Field.P, e0, f1);
SecP224R1Field.Multiply(f1, d0, f1);
SecP224R1Field.Square(f1, d1);
return(Nat224.Eq(c, d1) ? new SecP224R1FieldElement(f1) : null);
}
}
// Avoid any possible infinite loop due to a bad random number generator
SecP224R1Field.AddOne(r, r);
}
}
public override ECFieldElement Sqrt()
{
uint[] x = this.x;
if (Nat224.IsZero(x) || Nat224.IsOne(x))
{
return(this);
}
uint[] z = Nat224.Create();
SecP224R1Field.Negate(x, z);
uint[] r = Mod.Random(SecP224R1Field.P);
uint[] t = Nat224.Create();
if (!IsSquare(x))
{
return(null);
}
while (!TrySqrt(z, r, t))
{
SecP224R1Field.AddOne(r, r);
}
SecP224R1Field.Square(t, r);
return(!Nat224.Eq(x, r) ? null : new SecP224R1FieldElement(t));
}
public override ECFieldElement Sqrt()
{
uint[] array = x;
if (Nat224.IsZero(array) || Nat224.IsOne(array))
{
return(this);
}
uint[] array2 = Nat224.Create();
SecP224R1Field.Negate(array, array2);
uint[] array3 = Mod.Random(SecP224R1Field.P);
uint[] t = Nat224.Create();
if (!IsSquare(array))
{
return(null);
}
while (!TrySqrt(array2, array3, t))
{
SecP224R1Field.AddOne(array3, array3);
}
SecP224R1Field.Square(t, array3);
return((!Nat224.Eq(array, array3)) ? null : new SecP224R1FieldElement(t));
}
/**
* return a sqrt root - the routine verifies that the calculation returns the right value - if
* none exists it returns null.
*/
public override ECFieldElement Sqrt()
{
uint[] c = this.x;
if (Nat224.IsZero(c) || Nat224.IsOne(c))
return this;
uint[] nc = Nat224.Create();
SecP224R1Field.Negate(c, nc);
uint[] r = Mod.Random(SecP224R1Field.P);
uint[] t = Nat224.Create();
if (!IsSquare(c))
return null;
while (!TrySqrt(nc, r, t))
{
SecP224R1Field.AddOne(r, r);
}
SecP224R1Field.Square(t, r);
return Nat224.Eq(c, r) ? new SecP224R1FieldElement(t) : null;
}
/**
* return a sqrt root - the routine verifies that the calculation returns the right value - if
* none exists it returns null.
*/
public override ECFieldElement Sqrt()
{
/*
* Q == 8m + 5, so we use Pocklington's method for this case.
*
* First, raise this element to the exponent 2^221 - 2^29 - 2^9 - 2^8 - 2^6 - 2^4 - 2^1 (i.e. m + 1)
*
* Breaking up the exponent's binary representation into "repunits", we get:
* { 191 1s } { 1 0s } { 19 1s } { 2 0s } { 1 1s } { 1 0s } { 1 1s } { 1 0s } { 3 1s } { 1 0s }
*
* Therefore we need an addition chain containing 1, 3, 19, 191 (the lengths of the repunits)
* We use: [1], 2, [3], 4, 8, 11, [19], 23, 42, 84, 107, [191]
*/
uint[] x1 = this.x;
if (Nat224.IsZero(x1) || Nat224.IsOne(x1))
{
return(this);
}
uint[] x2 = Nat224.Create();
SecP224K1Field.Square(x1, x2);
SecP224K1Field.Multiply(x2, x1, x2);
uint[] x3 = x2;
SecP224K1Field.Square(x2, x3);
SecP224K1Field.Multiply(x3, x1, x3);
uint[] x4 = Nat224.Create();
SecP224K1Field.Square(x3, x4);
SecP224K1Field.Multiply(x4, x1, x4);
uint[] x8 = Nat224.Create();
SecP224K1Field.SquareN(x4, 4, x8);
SecP224K1Field.Multiply(x8, x4, x8);
uint[] x11 = Nat224.Create();
SecP224K1Field.SquareN(x8, 3, x11);
SecP224K1Field.Multiply(x11, x3, x11);
uint[] x19 = x11;
SecP224K1Field.SquareN(x11, 8, x19);
SecP224K1Field.Multiply(x19, x8, x19);
uint[] x23 = x8;
SecP224K1Field.SquareN(x19, 4, x23);
SecP224K1Field.Multiply(x23, x4, x23);
uint[] x42 = x4;
SecP224K1Field.SquareN(x23, 19, x42);
SecP224K1Field.Multiply(x42, x19, x42);
uint[] x84 = Nat224.Create();
SecP224K1Field.SquareN(x42, 42, x84);
SecP224K1Field.Multiply(x84, x42, x84);
uint[] x107 = x42;
SecP224K1Field.SquareN(x84, 23, x107);
SecP224K1Field.Multiply(x107, x23, x107);
uint[] x191 = x23;
SecP224K1Field.SquareN(x107, 84, x191);
SecP224K1Field.Multiply(x191, x84, x191);
uint[] t1 = x191;
SecP224K1Field.SquareN(t1, 20, t1);
SecP224K1Field.Multiply(t1, x19, t1);
SecP224K1Field.SquareN(t1, 3, t1);
SecP224K1Field.Multiply(t1, x1, t1);
SecP224K1Field.SquareN(t1, 2, t1);
SecP224K1Field.Multiply(t1, x1, t1);
SecP224K1Field.SquareN(t1, 4, t1);
SecP224K1Field.Multiply(t1, x3, t1);
SecP224K1Field.Square(t1, t1);
uint[] t2 = x84;
SecP224K1Field.Square(t1, t2);
if (Nat224.Eq(x1, t2))
{
return(new SecP224K1FieldElement(t1));
}
/*
* If the first guess is incorrect, we multiply by a precomputed power of 2 to get the second guess,
* which is ((4x)^(m + 1))/2 mod Q
*/
SecP224K1Field.Multiply(t1, PRECOMP_POW2, t1);
SecP224K1Field.Square(t1, t2);
if (Nat224.Eq(x1, t2))
{
return(new SecP224K1FieldElement(t1));
}
return(null);
}
public override ECFieldElement Sqrt()
{
uint[] y = this.x;
if (Nat224.IsZero(y) || Nat224.IsOne(y))
{
return(this);
}
uint[] array = Nat224.Create();
SecP224K1Field.Square(y, array);
SecP224K1Field.Multiply(array, y, array);
uint[] array2 = array;
SecP224K1Field.Square(array, array2);
SecP224K1Field.Multiply(array2, y, array2);
uint[] array3 = Nat224.Create();
SecP224K1Field.Square(array2, array3);
SecP224K1Field.Multiply(array3, y, array3);
uint[] array4 = Nat224.Create();
SecP224K1Field.SquareN(array3, 4, array4);
SecP224K1Field.Multiply(array4, array3, array4);
uint[] array5 = Nat224.Create();
SecP224K1Field.SquareN(array4, 3, array5);
SecP224K1Field.Multiply(array5, array2, array5);
uint[] array6 = array5;
SecP224K1Field.SquareN(array5, 8, array6);
SecP224K1Field.Multiply(array6, array4, array6);
uint[] array7 = array4;
SecP224K1Field.SquareN(array6, 4, array7);
SecP224K1Field.Multiply(array7, array3, array7);
uint[] array8 = array3;
SecP224K1Field.SquareN(array7, 19, array8);
SecP224K1Field.Multiply(array8, array6, array8);
uint[] array9 = Nat224.Create();
SecP224K1Field.SquareN(array8, 42, array9);
SecP224K1Field.Multiply(array9, array8, array9);
uint[] z = array8;
SecP224K1Field.SquareN(array9, 23, z);
SecP224K1Field.Multiply(z, array7, z);
uint[] array10 = array7;
SecP224K1Field.SquareN(z, 84, array10);
SecP224K1Field.Multiply(array10, array9, array10);
uint[] z2 = array10;
SecP224K1Field.SquareN(z2, 20, z2);
SecP224K1Field.Multiply(z2, array6, z2);
SecP224K1Field.SquareN(z2, 3, z2);
SecP224K1Field.Multiply(z2, y, z2);
SecP224K1Field.SquareN(z2, 2, z2);
SecP224K1Field.Multiply(z2, y, z2);
SecP224K1Field.SquareN(z2, 4, z2);
SecP224K1Field.Multiply(z2, array2, z2);
SecP224K1Field.Square(z2, z2);
uint[] array11 = array9;
SecP224K1Field.Square(z2, array11);
if (Nat224.Eq(y, array11))
{
return(new SecP224K1FieldElement(z2));
}
SecP224K1Field.Multiply(z2, SecP224K1FieldElement.PRECOMP_POW2, z2);
SecP224K1Field.Square(z2, array11);
if (Nat224.Eq(y, array11))
{
return(new SecP224K1FieldElement(z2));
}
return(null);
}
public override ECFieldElement Sqrt()
{
uint[] x = this.x;
if (Nat224.IsZero(x) || Nat224.IsOne(x))
{
return(this);
}
uint[] z = Nat224.Create();
SecP224K1Field.Square(x, z);
SecP224K1Field.Multiply(z, x, z);
uint[] numArray3 = z;
SecP224K1Field.Square(z, numArray3);
SecP224K1Field.Multiply(numArray3, x, numArray3);
uint[] numArray4 = Nat224.Create();
SecP224K1Field.Square(numArray3, numArray4);
SecP224K1Field.Multiply(numArray4, x, numArray4);
uint[] numArray5 = Nat224.Create();
SecP224K1Field.SquareN(numArray4, 4, numArray5);
SecP224K1Field.Multiply(numArray5, numArray4, numArray5);
uint[] numArray6 = Nat224.Create();
SecP224K1Field.SquareN(numArray5, 3, numArray6);
SecP224K1Field.Multiply(numArray6, numArray3, numArray6);
uint[] numArray7 = numArray6;
SecP224K1Field.SquareN(numArray6, 8, numArray7);
SecP224K1Field.Multiply(numArray7, numArray5, numArray7);
uint[] numArray8 = numArray5;
SecP224K1Field.SquareN(numArray7, 4, numArray8);
SecP224K1Field.Multiply(numArray8, numArray4, numArray8);
uint[] numArray9 = numArray4;
SecP224K1Field.SquareN(numArray8, 0x13, numArray9);
SecP224K1Field.Multiply(numArray9, numArray7, numArray9);
uint[] numArray10 = Nat224.Create();
SecP224K1Field.SquareN(numArray9, 0x2a, numArray10);
SecP224K1Field.Multiply(numArray10, numArray9, numArray10);
uint[] numArray11 = numArray9;
SecP224K1Field.SquareN(numArray10, 0x17, numArray11);
SecP224K1Field.Multiply(numArray11, numArray8, numArray11);
uint[] numArray12 = numArray8;
SecP224K1Field.SquareN(numArray11, 0x54, numArray12);
SecP224K1Field.Multiply(numArray12, numArray10, numArray12);
uint[] numArray13 = numArray12;
SecP224K1Field.SquareN(numArray13, 20, numArray13);
SecP224K1Field.Multiply(numArray13, numArray7, numArray13);
SecP224K1Field.SquareN(numArray13, 3, numArray13);
SecP224K1Field.Multiply(numArray13, x, numArray13);
SecP224K1Field.SquareN(numArray13, 2, numArray13);
SecP224K1Field.Multiply(numArray13, x, numArray13);
SecP224K1Field.SquareN(numArray13, 4, numArray13);
SecP224K1Field.Multiply(numArray13, numArray3, numArray13);
SecP224K1Field.Square(numArray13, numArray13);
uint[] numArray14 = numArray10;
SecP224K1Field.Square(numArray13, numArray14);
if (Nat224.Eq(x, numArray14))
{
return(new SecP224K1FieldElement(numArray13));
}
SecP224K1Field.Multiply(numArray13, PRECOMP_POW2, numArray13);
SecP224K1Field.Square(numArray13, numArray14);
if (Nat224.Eq(x, numArray14))
{
return(new SecP224K1FieldElement(numArray13));
}
return(null);
}